Azimuth Calculator
Find the true azimuth, the compass direction you must face to travel the shortest path from one point on Earth to another.
🌍 What is Azimuth?
Azimuth is the horizontal angle, measured clockwise from true north, that points from one location toward another. It runs from 0 degrees at due north, through 90 degrees at due east, 180 degrees at due south and 270 degrees at due west, wrapping back to 360 at north again. When you calculate the azimuth between two points given as latitude and longitude, you are asking a spherical trigonometry question: in which direction must I set off so that the great circle I follow, the shortest path across the surface of a sphere, ends at my destination?
Azimuth is used constantly in practical work. Aviators use it to plan great-circle routes between airports and to set an initial heading before a flight management system takes over. Surveyors use it to orient a traverse against a known reference line, since every leg of a survey is recorded as a distance plus an azimuth. Satellite installers use it to swing a dish toward a geostationary slot, paired with an elevation angle. Antenna riggers use it to point a directional yagi at a distant repeater, and amateur radio operators use it to aim at another station for long-distance contacts. Hikers and orienteers use it to translate a map line into a compass heading they can actually walk.
The most common misconception is that azimuth is constant along a route. It is not. Except for paths that run exactly along the equator or exactly along one meridian, a great circle crosses each meridian at a different angle, so the bearing to your destination drifts steadily as you travel. This is exactly why a New York to Tokyo flight path arches up over the Arctic on a flat Mercator map while still being the shortest possible route. A second misconception is that the value a compass shows is the same number this calculator produces. A magnetic compass reads magnetic azimuth, which differs from true azimuth by the local magnetic declination, sometimes by more than 20 degrees at high latitudes.
This calculator takes two coordinate pairs in decimal degrees and returns the initial azimuth, the matching 16-point compass label, the final azimuth you would be flying or sailing on at arrival, and the back azimuth that points straight back the way you came. It also charts how the bearing to your destination changes over the course of the journey, so the great-circle drift becomes visible rather than abstract.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — New York to London
Start 40.7128°N, 74.0060°W → destination 51.5074°N, 0.1278°W
Example 2 — Sydney to Tokyo
Start 33.8688°S, 151.2093°E → destination 35.6762°N, 139.6503°E
Example 3 — Cape Town to Rio de Janeiro
Start 33.9249°S, 18.4241°E → destination 22.9068°S, 43.1729°W
❓ Frequently Asked Questions
🔗 Related Calculators
What is an azimuth in navigation?
An azimuth is a horizontal angle measured clockwise from a north reference line to the direction of an object or destination, expressed in degrees from 0 to 360. In navigation and surveying it tells you which way to face or point to travel toward a target, with 0 degrees meaning due north and 90 degrees meaning due east.
What is the formula for azimuth between two coordinates?
The spherical initial bearing formula is theta = atan2(sin(dLon) * cos(lat2), cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon)), where dLon is the longitude difference. Convert the result from radians to degrees and add 360 then take the remainder by 360 so the answer falls in the 0 to 360 range.
What is the difference between azimuth and bearing?
In everyday use they are interchangeable, but strictly an azimuth is always a full-circle value from 0 to 360 degrees measured clockwise from north, while a bearing is often written in quadrant form such as N 45 E. This calculator reports the full-circle azimuth form.
What is a back azimuth and how do I calculate it?
A back azimuth points in the exact opposite direction to a forward azimuth. Add 180 degrees if the forward azimuth is less than 180, or subtract 180 if it is 180 or more. A forward azimuth of 51.21 degrees gives a back azimuth of 231.21 degrees.
Why does the azimuth change along a great-circle route?
A great circle crosses every meridian at a different angle, so the bearing to your destination shifts continuously as you travel. Only routes along the equator or along a single meridian keep a constant azimuth. The chart on this page plots that drift for the route you entered.
Is this true azimuth or magnetic azimuth?
This calculator returns true azimuth, measured from the geographic north pole. To convert it to a magnetic compass heading you must apply the local magnetic declination, which varies by location and drifts over time by roughly a tenth of a degree per year in many regions.
How accurate is the spherical azimuth formula?
Treating Earth as a perfect sphere introduces an error of up to about 0.2 degrees on very long routes, because Earth is an oblate spheroid flattened by about 1 part in 298. For surveying-grade accuracy, use a geodesic method such as Vincenty's or Karney's algorithm on the WGS-84 ellipsoid.
What compass direction does an azimuth of 264 degrees correspond to?
264 degrees falls within the 16-point compass sector centred on west (270 degrees), which spans 258.75 to 281.25 degrees, so it is labelled W. Each of the 16 named compass points covers a 22.5 degree sector centred on its nominal bearing.
How do I enter southern and western coordinates?
Use negative decimal degrees. South latitudes and west longitudes are negative, so Sydney is entered as -33.8688 latitude and 151.2093 longitude, while Rio de Janeiro is -22.9068 latitude and -43.1729 longitude.
Can I use azimuth to aim a satellite dish or solar panel?
Yes, azimuth is one of the two pointing angles used for dishes and trackers, the other being elevation. Compute the azimuth from your site to the target ground point, then correct for magnetic declination if you are aiming with a handheld compass rather than a GPS-referenced mount.
What is the final azimuth shown by this calculator?
The final azimuth is the heading you would be travelling on at the moment you arrive at the destination, which differs from the initial azimuth on any route that is not along the equator or a single meridian. New York to London starts at 51.21 degrees and arrives on a heading of 108.33 degrees.
Does azimuth depend on which point I enter first?
Yes. Azimuth is directional, so swapping the start and destination generally gives a completely different value, not simply the reverse. The azimuth from London back to New York is not 231.21 degrees, because the great circle meets the meridians at different angles at each end.